Gaming devices are a significant source of revenue for casinos, and casinos continue to search for new ways to attract players to such devices. Most gaming devices, including video poker devices and other slot machines, allow players to wager on various game outcomes. A typical video poker device receives a wager amount from a player and generates an initial hand of five cards that are drawn from a “deck” of fifty-two different cards. Each card has a suit (clubs, spades, hearts or diamonds) and a rank (2–10, Jack, Queen, King, or Ace).
The player then selects which cards, if any, he would like to “hold”. The player may hold anywhere from no cards to all five cards. Cards that are not held are discarded (removed from the initial hand) and replaced with an equal number of new cards that are drawn from the deck of forty-seven remaining cards (52−5=47).
The cards that are selected to be held define a “draw strategy”. For example, if the first and third cards are held, then the corresponding draw strategy is to discard the second, fourth and fifth cards and draw three new cards to replace them. After new cards are drawn, a second hand results. The second hand is different from the initial hand unless all five cards are held (no cards are drawn). Since each of the five cards in the hand may either be held or not held (i.e. two choices per card), each initial hand defines thirty-two draw strategies (2*2*2*2*2=32). Similarly, each draw strategy defines a set of possible second hands. For example, if the draw strategy is to hold the first four cards (draw one card to replace the fifth), then that draw strategy defines forty-seven possible second hands (the one card drawn may be one of forty-seven cards in the deck). Each of these forty-seven possible second hands includes the first four cards of the initial hand, and also includes a fifth card that is selected from the deck. In another example, if the draw strategy is to hold all cards (draw no cards), then that draw strategy defines one possible second hand, which is the same as the initial hand.
If the second hand is a type of “winning hand”, the player is awarded a payment amount that is based on the winning hand and the wager amount. A “hand grouping” defines one or more winning hands that share a characteristic. For example, the hand grouping “four of a kind”, defines several winning hands, each of which has four cards of the same rank. The following three winning hands are included in the set defined by the hand grouping “four of a kind”:    J-hearts, J-diamonds, J-clubs, J-spades, 7-clubs    7-clubs, 8-hearts, 8-diamonds, 8-clubs, 8-spades    J-hearts, J-diamonds, 3-diamonds, J-clubs, J-spadesSimilarly, the hand grouping “royal flush” defines four winning hands:    10-hearts, Jack-hearts, Queen-hearts, King-hearts, Ace-hearts    10-diamonds, Jack-diamonds, Queen-diamonds, King-diamonds, Ace-diamonds    10-spades, Jack-spades, Queen-spades, King-spades, Ace-spades    10-clubs, Jack-clubs, Queen-clubs, King-clubs, Ace-clubs.
In video poker, the arrangement of the cards within a hand is ignored. Some hand groupings are mutually exclusive. Thus, a hand included in one such hand grouping cannot be included in another such hand grouping. For example, a hand:    10-diamonds, Jack-diamonds, King-diamonds, Queen-diamonds, Ace-diamondsis included in the set defined by “royal flush”, but not in the set defined by “flush”.
Typically, each hand grouping has a corresponding payout ratio that defines an amount of payment won for each unit of a wager amount. If the second hand is a winning hand, then the hand grouping corresponding to that hand indicates a payout ratio, and the payout ratio multiplied by the wager amount is the payment awarded. For example, if the second hand is:    Ace-hearts, 3-hearts, 7-hearts, 5-hearts, 10-heartsthen the corresponding hand grouping is a “flush” (all cards have the same suit). If “flush” has a corresponding payout ratio of six, then the payment amount is six times the wager amount.
Each draw strategy has an expected value which generally indicates the average payout that will be received if a draw strategy is chosen for a first hand. The expected value of a draw strategy may be calculated as the sum of the products of the probability of receiving each possible second hand times the payment amount won (if any) for receiving each possible second hand. The optimum draw strategy is the draw strategy having the highest expected value.
For example, a player dealt a first hand of    King-diamonds, King-spades, 8-hearts, 8-clubs, 2-clubsmay select the draw strategy of holding the two Kings and the two 8's, and discarding the 2-clubs. Consequently, only two hand groupings are possible: a full house (three cards with one rank and two cards with another rank) or two pair. The expected value of this draw strategy is the sum of the products of the probability of each hand grouping occurring multiplied by the payment received according to each hand grouping.
For the selected draw strategy, the second hand will be a “Full house” if the drawn card is a King or an 8, and two kings and two 8's remain in the deck of forty seven cards. Accordingly, the probability of a “Full House” is approximately 8.5% (4/47=0.085). Similarly, if any of the other cards are drawn from the deck, the second hand will be “Two Pair”. Accordingly, the probability of “Two Pair” is approximately 91.5% (43/47=0.915).
If the payout ratio for a “Full House” is “9” and the payout ratio for two pair is “2”, the expected value of the selected draw strategy may be calculated as follows:[0.085*9]+[0.915*2]=[0.766]+[1.83]=2.596.
Players who often (or always) choose “optimum” draw strategies (e.g., strategies having the highest expected value) for each initial hand generally tend to win somewhat higher average payment amounts from video poker devices than players who more often follow suboptimum strategies. Casinos generally would like to reduce the payout ratios so that the play of more skilled players (e.g., professional players, players generally employing optimum draw strategies) does not result in little profit for the casino (or even a loss). On the other hand, because players who typically employ suboptimum strategies receive lower payments on average than more skilled players, reducing the payout ratios may discourage less skilled players from playing.
U.S. Pat. No. 5,511,781 to Wood et al. describes a game system that calculates the expected value of elements (e.g., cards) a player currently possesses. The expected value is used to set the size of a guaranteed award provided if the player stops playing.
U.S. Pat. No. 5,401,023 to Wood describes a video poker game that calculates the optimum strategy from the expected value of each possible strategy. The video poker game computes the expected value of each discard strategy and then determines which discard strategy is the optimum strategy. If the player selects a strategy other than the optimum strategy, the award values for the hand groupings of cards are adjusted so the expected value of the selected strategy is substantially equal to that of the optimum strategy. Thus, players who are not able to recognize what constitutes the optimum strategy for any given hand will win substantially the same amount of money over a long term as more skilled players who can recognize and play the optimum strategy for any given hand. The game displays the adjusted awards to the player after each strategy is selected. This permits the player to evaluate the possible strategies.